Speed sensors play critical role in induction motor (IM) control systems. However, the use of these sensors cause several drawbacks such as increasing the overall cost, decreased reliability on control and increased noise problems in data acquisition. The sensorless control methods also have been proposed in control systems of IM to increase the overall performance. On the other hand, model predictive controllers (MPCs) which is one of the most recently used controller methods require the speed measurement to perform speed and torque control of an IM. In addition to control method, the topology of voltage source inverter (VSI) affects the overall efficiency of the IM drive because of its losses and total harmonic distortion (THD) ratios delivered by the topology. The main proposal of this study is to implement an IM drive built with a three-level active neutral point clamped (3L-ANPC) voltage source inverter (VSI) and to propose an MPC that eliminates sensor requirement in speed control of IM. The proposed IM drive takes benefits of multilevel inverter topology, which reduces the torque ripple, enables low switching frequency and provides decreased harmonic distortion. The switching pulses of ANPC VSI are generated by the proposed sensorless MPC method for controlling the torque of IM. The modelling and experimental verification of the ANPC based IM drive have been carried out and the sensorless MPC controller has been validated in this study. There two types of model reference adaptive system (MRAS) have been proposed to ensure precise estimation of IM speed that should be supplied to MPC controller. These MRAS methods are titled as the rotor flux based model reference adaptive system (MRAS^F), and the stator current based model reference adaptive system (MRAS^CC) according to estimation references. The proposed MPC-based IM drive has been analyzed under variable speed and torque circumstances to detect the efficiency and reliability of MRAS^F and MRAS^CC algorithms. The efficiency indicators such as flux and torque responses, and speed control of the suggested MPC IM drive are validated with experimental analysis. The results of revealed that the IM effectively tracks the reference speed and produces the required torque depending to the precise control of proposed MPC algorithm.